QUESTION 1. Find the area. (Round to the nearest hundredth) QUESTION 2. Trapezoid QRST has two right angles. A 5in altitude can be drawn dividing QRST into a rectangle and an isosceles right triangle. The longer side of the rectangle measures 9in. What is the area of the trapezoid ?

The area of the trapezoid is 57.5 in.²

Step-by-step explanation:

The given information of the trapezoid are;

The vertices of the trapezoid = QRST

The altitude of the trapezoid = 5 in.

The shape the altitude divides the trapezoid into = A square and an isosceles right triangle

The long side of the rectangle = 9 in.

Therefore, we have;

The legs of an isosceles right triangle are equal

Given that one of the legs of the isosceles right triangle = The altitude of the triangle = 5 in.

Therefore, for the isosceles triangle, the length of the other leg = 5 in.

Therefore;

The area of the right triangle = 1/2 × Base × Height (altitude)

The area of the right triangle = 1/2 × Leg × leg = 1/2 × (Leg)²

∴ The area of the right triangle = 1/2 × 5 in. × 5 in. = 12.5 in.²

The length of the rectangle is given as l = 9 in.

The height of the rectangle, h = The altitude of the rectangle = 5 in.

The area of the rectangle, A = l × h

∴ The area of the rectangle, A = 9 in. × 5 in. = 45 in.²

The area of the trapezoid = The area of the right triangle + The area of the rectangle

The area of the trapezoid = 12.5 in.² + 45 in.² = 57.5 in.²

(8+64)^2= 5184 < answer

step-by-step explanation:

2^3 = 8

4^3= 64

(8+64)^2 = 5184